Ollie Banks bagged a brace to inspire the victory, with Armand Gnanduillet scoring the other goal in an emphatic victory.
Gnanduillet, Jay O’Shea and Ritchie Humphreys were the three changes made from the win against Daventry on Saturday.
Chesterfield started the game in the ascendency. With less than a minute on the clock, Ollie Banks had an effort for the Spireites, but his drilled effort just went wide of Josh Lillis’ goal.
Banks was finding a lot of space in front of the defence and unleashed another rasping effort which again just went the wrong side of the post.
Two audacious efforts followed for Chesterfield as O’Shea tried his luck from the half-way line, and Drew Talbot’s cross was awkward for the goalkeeper to deal with and almost found its way into the top corner.
As the game started to calm down, both sides started to enjoy spells of possession, without really creating many chances.
Banks was really having an influence on the game and five minutes before half time, he tried a delicate chip from 20 yards, but his effort narrowly sailed over the bar.
Just as the side’s looked to be heading into half time all square, the impressive Banks nodded Chesterfield’s first goal of the night. Roberts’ initial corner was cleared straight back to him, and he picked out the midfielder to powerfully head home from close range.
The second half started in very similar fashion to how the first ended. With the half only a minute old, Roberts crossed for Banks, but this time the midfielder couldn’t get his shot on target.
Five minutes later, Rochdale thought they had found an equaliser but the linesman’s flag prevented the goal. Ian Henderson put the ball past the onrushing Tommy Lee, but after much deliberation between the officials, the goal was ruled offside.
Henderson was causing the Spireites a threat down the left-hand side and he again nearly drew Rochdale level. The winger found time and unleashed an effort which smacked against the post and fortunately for Chesterfield, fell to safety.
From the breakaway, Roberts picked up the ball, drove at the defence and curled a shot towards the top corner but unfortunately the ball went the wrong side of the post.
Banks had been a constant menace for the Spireites as he was finding space and creating chances all night. The 21-year-old went close to doubling his tally on 70 minutes but his shot dragged wide.
Chesterfield struck again soon after through Frenchman, Gnanduillet. The influential Roberts found a lot of space out wide and delivered for the striker to double the lead.
The Spireites were in cruise control and it didn’t take them long to extend their advantage. Roberts and Banks were allowed a lot of freedom and the former FC United man grabbed his second of the game, comfortably lifting the ball past Lillis.
Both goalscorers, Banks and Gnanduillet left the field soon after to the applause of the crowd as they were replaced by Marc Richards and Tendayi Darikwa.
Henderson had a chance for the visitors late on, but Chesterfield goalkeeper, Lee was equal to the shot and it’s the Spireites that are in the hat for Saturday’s draw.
Chesterfield: Lee; Talbot, Evatt (c), Hird, Cooper; Ryan, Banks (Darikwa 80'), Humphreys, Roberts, O'Shea (Doyle 87'); Gnanduillet (Richards 80').
Subs not used: Chapman, Togwell.
Rochdale: Lillis; Eastham, Lancashire (c), Vincenti (Cummins 54'), Tutte (Allen 66'), Hogan, Vidal (Rose 17'), Done, O'Connell, Dicker, Henderson.
Subs not used: Thomson, Bunney.
Goals: Chesterfield (Banks 45+2', 78', Gnanduillet 72') 3 - 0 Rochdale
Attendance: 2,897 (174 Rochdale)